Fama French

4.4

a. 7 units of clothing

22 – 8 (1) = 14/2 = 7

b. Gabe to insert graph

c. The indifference curve is bowed in toward the origin.

Gabe to insert graph

d. Gabe to insert graph

e. Utility maximizing choice for clothing is 5 and 12 for food.

PcC + PfF = 22 C +1 = 1 F = 2C + 2

2C + F = 22 2 2

2C + 2C + 2 = 22

4C = 20

f. The MRS is ½ Gabe to insert graph

C + 1 = 1

F 2

g. Yes, Ann does have a diminishing marginal rate of substitution. Gabe to insert graph

As F (food on the x axis) increases, the slope gets smaller and smaller, therefore Ann is less and less willing to give up clothing units as her number of food units increases.

F = 3, slope is 1/3; F = 4, slope is ¼; F= 5, slope is 1/5, getting smaller as F (food on the x axis increases).

4. 5

The optimal consumption basket is y = .6 x = 42.8

3X = 5y 5x + 10y = 220

y = .6 5X + 10 (.6) = 220

x = 42.8

4.7

Ray is not maximizing his utility. He needs to consume fewer hamburgers and increase his consumption of root beer. Ray’s optimal consumption basket occurs (with his current income and prices of each good) at 1:2. Current consumption shows that Ray will trade 3 units root beer for 4 units of hamburger.

UMAX = 20 (2) + 15H = $100

H price = $4

MRS = MUrb = 6/8 = ¾ ≠ Prb = 2/4 = 1/2

MUH PH

4.12

a. Utility will be higher because Amy has more income to spend on more units of each good.

Before price change: (2) (10) + 2(2) = 24 After price change the number of units of each can increase for both goods, e.g. (1)(12) + (4) (3) = 24. Amy’s utility increases following the axiom that more is better.

b. No. Julie will save money no matter what and therefore have more money to spend on each good. It doesn’t matter as she can get positive utility out of the extra $6 of income she now has.

6.1

a. Average product of fertilizer is 550 roses per ton

2200/4 = 550 roses/ton

b. marginal product of 6th ton of fertilizer is 100

2600 – 2500 = 100 = 100

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